<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<b>assume </b><a NAME="E1:32"/><i><font color="Green">E8</font></i>: 
 <a href="polyeq_1.html#K7" target="_self">Polynom</a> 1,0,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<b>assume </b><a NAME="E2:32"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>5</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0 )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3;<br/>
<a NAME="E3:32"/><i><font color="Green">E10</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="polyeq_1.html#E1:32"><i><font color="Green">E8</font></i></a>, <a class="txt" href="polyeq_1.html#E2:32"><i><font color="Green">E9</font></i></a>, <a class="ref" href="polyeq_1.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E4:32"/><i><font color="Green">E11</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3
 
<b>by </b><i><a class="txt" href="polyeq_1.html#E1:32"><i><font color="Green">E8</font></i></a>, <a class="txt" href="polyeq_1.html#E2:32"><i><font color="Green">E9</font></i></a>, <a class="ref" href="polyeq_1.html#T18" target="_self">Th18</a></i>;<br/>
<div><i><font color="Green">E12</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E1:32"><i><font color="Green">E8</font></i></a>, <a class="txt" href="polyeq_1.html#E2:32"><i><font color="Green">E9</font></i></a>, <a class="ref" href="polyeq_1.html#T18" target="_self">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E1:32"><i><font color="Green">E8</font></i></a>, <a class="txt" href="polyeq_1.html#E2:32"><i><font color="Green">E9</font></i></a>, <a class="ref" href="polyeq_1.html#T18" target="_self">Th18</a></i>
;<br/></div><b>end;</b></div>
<b>set </b><font color="Maroon">c<sub>8</sub></font> = 1;<br/>
<b>set </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3;<br/>
<a NAME="E6:32"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span>
 
;<br/>
<a NAME="E7:32"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="polyeq_1.html#E5:32"><i><font color="Green">E12</font></i></a></i>;<br/>
<a NAME="E8:32"/><b>then </b><i><font color="Green">E13</font></i>: 
 <a href="polyeq_1.html#K3" target="_self">Polynom</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E9:32"/>
<font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> 
 
<b>by </b><i><a class="txt" href="polyeq_1.html#E3:32"><i><font color="Green">E10</font></i></a>, <a class="ref" href="square_1.html#T61">SQUARE_1:61</a></i>;<br/>
<b>then </b><i><font color="Green">E14</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E1:32"><i><font color="Green">E8</font></i></a>, <a class="txt" href="polyeq_1.html#E2:32"><i><font color="Green">E9</font></i></a>, <a class="ref" href="polyeq_1.html#T18" target="_self">Th18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> 

;<br/>
<a NAME="E11:32"/><b>then </b><i><font color="Green">E15</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/>
<a NAME="E12:32"/><b>then </b><i><font color="Green">E16</font></i>: 
 <a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="quin_1.html#D1">QUIN_1:def 1</a></i>;<br/>
<a NAME="E13:32"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> 0
 
;<br/>
<a NAME="E14:32"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="txt" href="polyeq_1.html#E5:32"><i><font color="Green">E12</font></i></a></i>;<br/>
<a NAME="E15:32"/><b>then </b><i><font color="Green">E17</font></i>: 
 <a href="polyeq_1.html#K3" target="_self">Polynom</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_3_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> or <font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> )
 </span><b>by </b><i><a class="txt" href="polyeq_1.html#E8:32"><i><font color="Green">E13</font></i></a>, <a class="txt" href="polyeq_1.html#E12:32"><i><font color="Green">E16</font></i></a>, <a class="ref" href="polyeq_1.html#T5" target="_self">Th5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1"><b>case </b></a><a NAME="E1:32_3_1_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:32_3_1_1"/><i><font color="Green">E19</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E10:32"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xreal_1.html#T65">XREAL_1:65</a></i>;<br/><i><font color="Green">E20</font></i>: <font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">4 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E1:32_3_1_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="quin_1.html#D1">QUIN_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="square_1.html#T85">SQUARE_1:85</a>, <a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="square_1.html#T99">SQUARE_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>

;<br/><i><font color="Green">E21</font></i>: <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

;<br/><b>then </b><i><font color="Green">E22</font></i>: <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>

;<br/><i><font color="Green">E23</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
;<br/><b>then </b><i><font color="Green">E24</font></i>: <font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E3:32_3_1_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="polyeq_1.html#E5:32_3_1_1"><i><font color="Green">E22</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>

;<br/><div><i><font color="Green">E25</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="32_3_1_1_6"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_6_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_3_1_1_6_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span><b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_6_1_1"><b>case </b></a><a NAME="E1:32_3_1_1_6_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_6_1_1"/><b>then </b><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="polyeq_1.html#E7:32_3_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E3:32_3_1_1_6_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E7:32_3_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>hence </b><a NAME="E4:32_3_1_1_6_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_1_6_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_6_1_2"><b>case </b></a><a NAME="E1:32_3_1_1_6_1_2"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_6_1_2"/><b>then </b><i><font color="Green">E27</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E7:32_3_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="newton.html#T16">NEWTON:16</a></i>;<br/><a NAME="E3:32_3_1_1_6_1_2"/><b>then </b>
3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>hence </b><a NAME="E4:32_3_1_1_6_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E1:32_3_1_1_6_1_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polyeq_1.html#E2:32_3_1_1_6_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_6_1_3"><b>case </b></a><a NAME="E1:32_3_1_1_6_1_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_6_1_3"/><b>then </b><i><font color="Green">E26</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/><span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

;<br/><a NAME="E4:32_3_1_1_6_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><b>then </b><i><font color="Green">E27</font></i>: <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>

<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>

;<br/><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>

;<br/><a NAME="E7:32_3_1_1_6_1_3"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E8:32_3_1_1_6_1_3"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E9:32_3_1_1_6_1_3"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E5:32_3_1_1_6_1_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E10:32_3_1_1_6_1_3"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_1_6_1_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E11:32_3_1_1_6_1_3"/><i><font color="Green">E31</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E7:32_3_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="polyeq_1.html#E2:32_3_1_1_6_1_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polyeq_1.html#E9:32_3_1_1_6_1_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E12:32_3_1_1_6_1_3"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E7:32_3_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="polyeq_1.html#E5:32_3_1_1_6_1_3"><i><font color="Green">E27</font></i></a>, <a class="txt" href="polyeq_1.html#E8:32_3_1_1_6_1_3"><i><font color="Green">E28</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E13:32_3_1_1_6_1_3"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E7:32_3_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="polyeq_1.html#E2:32_3_1_1_6_1_3"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polyeq_1.html#E10:32_3_1_1_6_1_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>;<br/><a NAME="E14:32_3_1_1_6_1_3"/><i><font color="Green">E33</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E11:32_3_1_1_6_1_3"><i><font color="Green">E31</font></i></a>, <a class="txt" href="polyeq_1.html#E13:32_3_1_1_6_1_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/><a NAME="E15:32_3_1_1_6_1_3"/><i><font color="Green">E34</font></i>: 
3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E16:32_3_1_1_6_1_3"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K2">-root</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E14:32_3_1_1_6_1_3"><i><font color="Green">E33</font></i></a>, <a class="ref" href="power.html#T12">POWER:12</a></i>;<br/><a NAME="E17:32_3_1_1_6_1_3"/>
3 <a href="power.html#K2">-root</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 <b>by </b><i><a class="txt" href="polyeq_1.html#E15:32_3_1_1_6_1_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="power.html#T9">POWER:9</a></i>;<br/><a NAME="E18:32_3_1_1_6_1_3"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E16:32_3_1_1_6_1_3"><i><font color="Green">E35</font></i></a></i>;<br/><b>hence </b><a NAME="E19:32_3_1_1_6_1_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_3_1_1_7"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_3_1_1_7_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> or <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> )
 </span><b>by </b><i><a class="txt" href="polyeq_1.html#E12:32"><i><font color="Green">E16</font></i></a>, <a class="txt" href="polyeq_1.html#E15:32"><i><font color="Green">E17</font></i></a>, <a class="ref" href="polyeq_1.html#T5" target="_self">Th5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1_1"><b>case </b></a><a NAME="E1:32_3_1_1_7_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_7_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">4 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="quin_1.html#D1">QUIN_1:def 1</a></i>;<br/><a NAME="E3:32_3_1_1_7_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> 4</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="square_1.html#T85">SQUARE_1:85</a>, <a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>;<br/><b>then </b><i><font color="Green">E26</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E11:32"><i><font color="Green">E15</font></i></a>, <a class="ref" href="square_1.html#T99">SQUARE_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>

;<br/><span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E4:32_3_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="power.html#T47">POWER:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

;<br/><b>then </b><i><font color="Green">E27</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E6:32_3_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="polyeq_1.html#E4:32_3_1_1_7_1_1"><i><font color="Green">E26</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>

;<br/><a NAME="E7:32_3_1_1_7_1_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_3_1_1_7_1_1_4"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1_1_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_3_1_1_7_1_1_4_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span><b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1_1_4_1_1"><b>case </b></a><a NAME="E1:32_3_1_1_7_1_1_4_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_7_1_1_4_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="polyeq_1.html#E7:32_3_1_1_7_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E3:32_3_1_1_7_1_1_4_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E6:32_3_1_1_7_1_1"><i><font color="Green">E27</font></i></a></i>;<br/><a NAME="E4:32_3_1_1_7_1_1_4_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_1_7_1_1_4_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>hence </b><a NAME="E5:32_3_1_1_7_1_1_4_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_1_7_1_1_4_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1_1_4_1_2"><b>case </b></a><a NAME="E1:32_3_1_1_7_1_1_4_1_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_7_1_1_4_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E6:32_3_1_1_7_1_1"><i><font color="Green">E27</font></i></a></i>;<br/><a NAME="E3:32_3_1_1_7_1_1_4_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E1:32_3_1_1_7_1_1_4_1_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="newton.html#T16">NEWTON:16</a></i>;<br/><b>hence </b><a NAME="E4:32_3_1_1_7_1_1_4_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E1:32_3_1_1_7_1_1_4_1_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="power.html#T6">POWER:6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1_1_4_1_3"><b>case </b></a><a NAME="E1:32_3_1_1_7_1_1_4_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_7_1_1_4_1_3"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/><a NAME="E3:32_3_1_1_7_1_1_4_1_3"/><b>then </b><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E4:32_3_1_1_7_1_1_4_1_3"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E5:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E6:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E7:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E8:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E9:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E10:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E11:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E12:32_3_1_1_7_1_1_4_1_3"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E13:32_3_1_1_7_1_1_4_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E14:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E15:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E16:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><a NAME="E17:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E18:32_3_1_1_7_1_1_4_1_3"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E19:32_3_1_1_7_1_1_4_1_3"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E7:32_3_1_1_7_1_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="polyeq_1.html#E3:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="polyeq_1.html#E12:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E31</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E20:32_3_1_1_7_1_1_4_1_3"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E7:32_3_1_1_7_1_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="polyeq_1.html#E12:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E31</font></i></a>, <a class="txt" href="polyeq_1.html#E18:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E21:32_3_1_1_7_1_1_4_1_3"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E29</font></i></a>, <a class="txt" href="polyeq_1.html#E3:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>;<br/><a NAME="E22:32_3_1_1_7_1_1_4_1_3"/><i><font color="Green">E35</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E19:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E33</font></i></a>, <a class="txt" href="polyeq_1.html#E21:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/><a NAME="E23:32_3_1_1_7_1_1_4_1_3"/><i><font color="Green">E36</font></i>: 
3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E24:32_3_1_1_7_1_1_4_1_3"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K2">-root</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E22:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="power.html#T12">POWER:12</a></i>;<br/><a NAME="E25:32_3_1_1_7_1_1_4_1_3"/>
3 <a href="power.html#K2">-root</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 <b>by </b><i><a class="txt" href="polyeq_1.html#E23:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E36</font></i></a>, <a class="ref" href="power.html#T9">POWER:9</a></i>;<br/><a NAME="E26:32_3_1_1_7_1_1_4_1_3"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E24:32_3_1_1_7_1_1_4_1_3"><i><font color="Green">E37</font></i></a></i>;<br/><b>hence </b><a NAME="E27:32_3_1_1_7_1_1_4_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E9:32_3_1_1_7_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32"><i><font color="Green">E9</font></i></a>, <a class="txt" href="polyeq_1.html#E8:32_3_1_1"><i><font color="Green">E25</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1_2"><b>case </b></a><a NAME="E1:32_3_1_1_7_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_7_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">4 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="quin_1.html#D1">QUIN_1:def 1</a></i>;<br/><a NAME="E3:32_3_1_1_7_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
 ;<br/><a NAME="E4:32_3_1_1_7_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
 ;<br/><a NAME="E5:32_3_1_1_7_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>
 ;<br/><a NAME="E6:32_3_1_1_7_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> 4</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="square_1.html#T85">SQUARE_1:85</a></i>;<br/><b>then </b><i><font color="Green">E26</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E11:32"><i><font color="Green">E15</font></i></a>, <a class="ref" href="square_1.html#T99">SQUARE_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>

;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_3_1_1_7_1_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_3_1_1_7_1_2_2_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span><b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1_2_2_1_1"><b>case </b></a><a NAME="E1:32_3_1_1_7_1_2_2_1_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_7_1_2_2_1_1"/><b>then </b><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E5:32_3_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="polyeq_1.html#E6:32_3_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="polyeq_1.html#E7:32_3_1_1_7_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E3:32_3_1_1_7_1_2_2_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="polyeq_1.html#E5:32_3_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="polyeq_1.html#E6:32_3_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="polyeq_1.html#E7:32_3_1_1_7_1_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polyeq_1.html#E1:32_3_1_1_7_1_2_2_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E4:32_3_1_1_7_1_2_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E5:32_3_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="polyeq_1.html#E6:32_3_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="polyeq_1.html#E7:32_3_1_1_7_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>hence </b><a NAME="E5:32_3_1_1_7_1_2_2_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_1_7_1_2_2_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1_2_2_1_2"><b>case </b></a><a NAME="E1:32_3_1_1_7_1_2_2_1_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_7_1_2_2_1_2"/><b>then </b><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E5:32_3_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="polyeq_1.html#E6:32_3_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="polyeq_1.html#E7:32_3_1_1_7_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="newton.html#T16">NEWTON:16</a></i>;<br/><b>hence </b><a NAME="E3:32_3_1_1_7_1_2_2_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E1:32_3_1_1_7_1_2_2_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>hence </b><a NAME="E4:32_3_1_1_7_1_2_2_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_1_7_1_2_2_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_1_7_1_2_2_1_3"><b>case </b></a><a NAME="E1:32_3_1_1_7_1_2_2_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_1_7_1_2_2_1_3"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/><a NAME="E3:32_3_1_1_7_1_2_2_1_3"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E4:32_3_1_1_7_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E5:32_3_1_1_7_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E6:32_3_1_1_7_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E7:32_3_1_1_7_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><b>then </b><i><font color="Green">E28</font></i>: <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>

<br/>.= 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>

;<br/><a NAME="E9:32_3_1_1_7_1_2_2_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E10:32_3_1_1_7_1_2_2_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E11:32_3_1_1_7_1_2_2_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E12:32_3_1_1_7_1_2_2_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><a NAME="E13:32_3_1_1_7_1_2_2_1_3"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E14:32_3_1_1_7_1_2_2_1_3"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="power.html#K3">to_power</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E15:32_3_1_1_7_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E8:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="polyeq_1.html#E13:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E16:32_3_1_1_7_1_2_2_1_3"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E5:32_3_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="polyeq_1.html#E6:32_3_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="polyeq_1.html#E7:32_3_1_1_7_1_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polyeq_1.html#E2:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E17:32_3_1_1_7_1_2_2_1_3"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E5:32_3_1_1"><i><font color="Green">E22</font></i></a>, <a class="txt" href="polyeq_1.html#E6:32_3_1_1"><i><font color="Green">E23</font></i></a>, <a class="txt" href="polyeq_1.html#E7:32_3_1_1_7_1_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polyeq_1.html#E8:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="polyeq_1.html#E13:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E29</font></i></a>, <a class="txt" href="polyeq_1.html#E14:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E18:32_3_1_1_7_1_2_2_1_3"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E27</font></i></a>, <a class="txt" href="polyeq_1.html#E16:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E31</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>;<br/><a NAME="E19:32_3_1_1_7_1_2_2_1_3"/><i><font color="Green">E33</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E16:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E31</font></i></a>, <a class="txt" href="polyeq_1.html#E18:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/><a NAME="E20:32_3_1_1_7_1_2_2_1_3"/><i><font color="Green">E34</font></i>: 
3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E21:32_3_1_1_7_1_2_2_1_3"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K2">-root</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E19:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E33</font></i></a>, <a class="ref" href="power.html#T12">POWER:12</a></i>;<br/><a NAME="E22:32_3_1_1_7_1_2_2_1_3"/>
3 <a href="power.html#K2">-root</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 <b>by </b><i><a class="txt" href="polyeq_1.html#E20:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="power.html#T9">POWER:9</a></i>;<br/><a NAME="E23:32_3_1_1_7_1_2_2_1_3"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E21:32_3_1_1_7_1_2_2_1_3"><i><font color="Green">E35</font></i></a></i>;<br/><b>hence </b><a NAME="E24:32_3_1_1_7_1_2_2_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E9:32_3_1_1_7_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32"><i><font color="Green">E9</font></i></a>, <a class="txt" href="polyeq_1.html#E8:32_3_1_1"><i><font color="Green">E25</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E10:32_3_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2"><b>case </b></a><a NAME="E1:32_3_1_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:32_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">4 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="quin_1.html#D1">QUIN_1:def 1</a></i>;<br/><b>then </b><i><font color="Green">E19</font></i>: <font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="square_1.html#T85">SQUARE_1:85</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E11:32"><i><font color="Green">E15</font></i></a>, <a class="ref" href="square_1.html#T99">SQUARE_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>

;<br/><b>hence </b><a NAME="E4:32_3_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E5:32_3_1_2"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E6:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E7:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E8:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E9:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E10:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E11:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E12:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E13:32_3_1_2"/><b>then </b><i><font color="Green">E20</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E14:32_3_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E15:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E16:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E17:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>
 ;<br/><a NAME="E18:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E19:32_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E20:32_3_1_2"/><b>then </b><i><font color="Green">E21</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E13:32_3_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="32_3_1_2_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_3_1_2_2_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span><b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_2_1_1"><b>case </b></a><a NAME="E1:32_3_1_2_2_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_2_1_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E3:32_3_1_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="polyeq_1.html#E20:32_3_1_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E3:32_3_1_2_2_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="polyeq_1.html#E3:32_3_1_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="polyeq_1.html#E20:32_3_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="polyeq_1.html#E1:32_3_1_2_2_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E4:32_3_1_2_2_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E3:32_3_1_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="polyeq_1.html#E20:32_3_1_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>hence </b><a NAME="E5:32_3_1_2_2_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_2_2_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_2_1_2"><b>case </b></a><a NAME="E1:32_3_1_2_2_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_2_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E3:32_3_1_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="polyeq_1.html#E20:32_3_1_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="newton.html#T16">NEWTON:16</a></i>;<br/><b>hence </b><a NAME="E3:32_3_1_2_2_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E1:32_3_1_2_2_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="power.html#T6">POWER:6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_2_1_3"><b>case </b></a><a NAME="E1:32_3_1_2_2_1_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_2_1_3"/><b>then </b><i><font color="Green">E23</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/><a NAME="E3:32_3_1_2_2_1_3"/><b>then </b><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E4:32_3_1_2_2_1_3"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E5:32_3_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E6:32_3_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E7:32_3_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E8:32_3_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E9:32_3_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E10:32_3_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E11:32_3_1_2_2_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E12:32_3_1_2_2_1_3"/><b>then </b><i><font color="Green">E25</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E13:32_3_1_2_2_1_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E14:32_3_1_2_2_1_3"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E15:32_3_1_2_2_1_3"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E16:32_3_1_2_2_1_3"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/><a NAME="E17:32_3_1_2_2_1_3"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E18:32_3_1_2_2_1_3"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E19:32_3_1_2_2_1_3"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E3:32_3_1_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="polyeq_1.html#E20:32_3_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="polyeq_1.html#E3:32_3_1_2_2_1_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="polyeq_1.html#E12:32_3_1_2_2_1_3"><i><font color="Green">E25</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E20:32_3_1_2_2_1_3"/><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E3:32_3_1_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="polyeq_1.html#E20:32_3_1_2"><i><font color="Green">E21</font></i></a>, <a class="txt" href="polyeq_1.html#E12:32_3_1_2_2_1_3"><i><font color="Green">E25</font></i></a>, <a class="txt" href="polyeq_1.html#E18:32_3_1_2_2_1_3"><i><font color="Green">E26</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E21:32_3_1_2_2_1_3"/><i><font color="Green">E29</font></i>: 
3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E19:32_3_1_2_2_1_3"><i><font color="Green">E27</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/><b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>;<br/><a NAME="E22:32_3_1_2_2_1_3"/><i><font color="Green">E30</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_2_2_1_3"><i><font color="Green">E23</font></i></a>, <a class="txt" href="polyeq_1.html#E3:32_3_1_2_2_1_3"><i><font color="Green">E24</font></i></a>, <a class="txt" href="polyeq_1.html#E20:32_3_1_2_2_1_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="polyeq_1.html#E21:32_3_1_2_2_1_3"><i><font color="Green">E29</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><a NAME="E23:32_3_1_2_2_1_3"/><i><font color="Green">E31</font></i>: 
3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E24:32_3_1_2_2_1_3"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K2">-root</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E22:32_3_1_2_2_1_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="power.html#T12">POWER:12</a></i>;<br/><a NAME="E25:32_3_1_2_2_1_3"/>
3 <a href="power.html#K2">-root</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 <b>by </b><i><a class="txt" href="polyeq_1.html#E23:32_3_1_2_2_1_3"><i><font color="Green">E31</font></i></a>, <a class="ref" href="power.html#T9">POWER:9</a></i>;<br/><a NAME="E26:32_3_1_2_2_1_3"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E24:32_3_1_2_2_1_3"><i><font color="Green">E32</font></i></a></i>;<br/><b>hence </b><a NAME="E27:32_3_1_2_2_1_3"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_3_1_2_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_3_1_2_3_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> or <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> )
 </span><b>by </b><i><a class="txt" href="polyeq_1.html#E12:32"><i><font color="Green">E16</font></i></a>, <a class="txt" href="polyeq_1.html#E15:32"><i><font color="Green">E17</font></i></a>, <a class="ref" href="polyeq_1.html#T5" target="_self">Th5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1_1"><b>case </b></a><a NAME="E1:32_3_1_2_3_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">4 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="quin_1.html#D1">QUIN_1:def 1</a></i>;<br/><a NAME="E3:32_3_1_2_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> 4</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="square_1.html#T85">SQUARE_1:85</a>, <a class="ref" href="xcmplx_1.html#T63">XCMPLX_1:63</a></i>;<br/><b>then </b><i><font color="Green">E23</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E11:32"><i><font color="Green">E15</font></i></a>, <a class="ref" href="square_1.html#T99">SQUARE_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>

;<br/><a NAME="E5:32_3_1_2_3_1_1"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E6:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E7:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E8:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span></span>)</span>
 ;<br/><a NAME="E9:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E10:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E11:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E12:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E13:32_3_1_2_3_1_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E14:32_3_1_2_3_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E15:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E16:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E17:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>
 ;<br/><a NAME="E18:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E19:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E20:32_3_1_2_3_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E13:32_3_1_2_3_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><b>then </b><i><font color="Green">E25</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E4:32_3_1_2_3_1_1"><i><font color="Green">E23</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>

;<br/><a NAME="E22:32_3_1_2_3_1_1"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_3_1_2_3_1_1_3"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_3_1_2_3_1_1_3_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span><b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1_1_3_1_1"><b>case </b></a><a NAME="E1:32_3_1_2_3_1_1_3_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_3_1_1_3_1_1"/><b>then </b><i><font color="Green">E27</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="polyeq_1.html#E22:32_3_1_2_3_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E3:32_3_1_2_3_1_1_3_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E22:32_3_1_2_3_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>hence </b><a NAME="E4:32_3_1_2_3_1_1_3_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_2_3_1_1_3_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1_1_3_1_2"><b>case </b></a><a NAME="E1:32_3_1_2_3_1_1_3_1_2"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_3_1_1_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E22:32_3_1_2_3_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="newton.html#T16">NEWTON:16</a></i>;<br/><b>hence </b><a NAME="E3:32_3_1_2_3_1_1_3_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E1:32_3_1_2_3_1_1_3_1_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="power.html#T6">POWER:6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1_1_3_1_3"><b>case </b></a><a NAME="E1:32_3_1_2_3_1_1_3_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_3_1_1_3_1_3"/><b>then </b><i><font color="Green">E27</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/><a NAME="E3:32_3_1_2_3_1_1_3_1_3"/><b>then </b><i><font color="Green">E28</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E4:32_3_1_2_3_1_1_3_1_3"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E5:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E6:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E7:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E8:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E9:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E10:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E11:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E12:32_3_1_2_3_1_1_3_1_3"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
 ;<br/><a NAME="E13:32_3_1_2_3_1_1_3_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>
 ;<br/><a NAME="E14:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E15:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>;<br/><a NAME="E16:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
 ;<br/><a NAME="E17:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 ;<br/><a NAME="E18:32_3_1_2_3_1_1_3_1_3"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E19:32_3_1_2_3_1_1_3_1_3"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E20:32_3_1_2_3_1_1_3_1_3"/><i><font color="Green">E32</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E22:32_3_1_2_3_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polyeq_1.html#E3:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E28</font></i></a>, <a class="txt" href="polyeq_1.html#E12:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E29</font></i></a>, <a class="txt" href="polyeq_1.html#E18:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E30</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E21:32_3_1_2_3_1_1_3_1_3"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E21:32_3_1_2_3_1_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="polyeq_1.html#E12:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E29</font></i></a>, <a class="txt" href="polyeq_1.html#E19:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E31</font></i></a></i>;<br/><a NAME="E22:32_3_1_2_3_1_1_3_1_3"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E27</font></i></a>, <a class="txt" href="polyeq_1.html#E3:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E28</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>;<br/><a NAME="E23:32_3_1_2_3_1_1_3_1_3"/><i><font color="Green">E34</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E20:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E32</font></i></a>, <a class="txt" href="polyeq_1.html#E22:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E33</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/><a NAME="E24:32_3_1_2_3_1_1_3_1_3"/><i><font color="Green">E35</font></i>: 
3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E25:32_3_1_2_3_1_1_3_1_3"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K2">-root</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E23:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="power.html#T12">POWER:12</a></i>;<br/><a NAME="E26:32_3_1_2_3_1_1_3_1_3"/>
3 <a href="power.html#K2">-root</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 <b>by </b><i><a class="txt" href="polyeq_1.html#E24:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="power.html#T9">POWER:9</a></i>;<br/><a NAME="E27:32_3_1_2_3_1_1_3_1_3"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E25:32_3_1_2_3_1_1_3_1_3"><i><font color="Green">E36</font></i></a></i>;<br/><b>hence </b><a NAME="E28:32_3_1_2_3_1_1_3_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E24:32_3_1_2_3_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32"><i><font color="Green">E9</font></i></a>, <a class="txt" href="polyeq_1.html#E21:32_3_1_2"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1_2"><b>case </b></a><a NAME="E1:32_3_1_2_3_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><a href="quin_1.html#K1">delta</a> 1,<font color="Maroon">c<sub>2</sub></font>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_3_1_2"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default">4 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="quin_1.html#D1">QUIN_1:def 1</a></i>;<br/><a NAME="E3:32_3_1_2_3_1_2"/>
<font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> 
 <b>by </b><i><a class="txt" href="polyeq_1.html#E3:32"><i><font color="Green">E10</font></i></a>, <a class="ref" href="square_1.html#T61">SQUARE_1:61</a></i>;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">4 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p1">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E4:32"><i><font color="Green">E11</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> 

;<br/><a NAME="E5:32_3_1_2_3_1_2"/><b>then </b>
 <a href="square_1.html#K6">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E1:32_3_1_2"><i><font color="Green">E18</font></i></a>, <a class="txt" href="polyeq_1.html#E1:32_3_1_2_3_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="square_1.html#T82">SQUARE_1:82</a></i>;<br/><a NAME="E6:32_3_1_2_3_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> 4</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_2_3_1_2"><i><font color="Green">E24</font></i></a></i>;<br/><b>then </b><i><font color="Green">E25</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p4">(<span class="default">4 <a href="xcmplx_0.html#K3">*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E11:32"><i><font color="Green">E15</font></i></a>, <a class="ref" href="square_1.html#T99">SQUARE_1:99</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default">1 <a href="xcmplx_0.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>

;<br/><span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span></span>)</span>

;<br/><b>then </b><span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

;<br/><a NAME="E10:32_3_1_2_3_1_2"/><b>then </b><i><font color="Green">E26</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
 ;<br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

;<br/><a NAME="E12:32_3_1_2_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E13:32_3_1_2_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E10:32_3_1_2_3_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><b>then </b><i><font color="Green">E27</font></i>: <font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="polyeq_1.html#E7:32_3_1_2_3_1_2"><i><font color="Green">E25</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p3">(<span class="default">2 <a href="real_1.html#K2">"</a> </span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>

;<br/><a NAME="E15:32_3_1_2_3_1_2"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_3_1_2_3_1_2_7"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1_2_7_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:32_3_1_2_3_1_2_7_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0 or <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0 )
 </span><b>by </b><i><a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1_2_7_1_1"><b>case </b></a><a NAME="E1:32_3_1_2_3_1_2_7_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_3_1_2_7_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 <b>by </b><i><a class="txt" href="polyeq_1.html#E15:32_3_1_2_3_1_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><a NAME="E3:32_3_1_2_3_1_2_7_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E14:32_3_1_2_3_1_2"><i><font color="Green">E27</font></i></a></i>;<br/><a NAME="E4:32_3_1_2_3_1_2_7_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_2_3_1_2_7_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>hence </b><a NAME="E5:32_3_1_2_3_1_2_7_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_2_3_1_2_7_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1_2_7_1_2"><b>case </b></a><a NAME="E1:32_3_1_2_3_1_2_7_1_2"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_3_1_2_7_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="ref" href="newton.html#T16">NEWTON:16</a></i>;<br/><a NAME="E3:32_3_1_2_3_1_2_7_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E14:32_3_1_2_3_1_2"><i><font color="Green">E27</font></i></a></i>;<br/><b>hence </b><a NAME="E4:32_3_1_2_3_1_2_7_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E1:32_3_1_2_3_1_2_7_1_2"><i><font color="Green">E29</font></i></a>, <a class="ref" href="power.html#T6">POWER:6</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="32_3_1_2_3_1_2_7_1_3"><b>case </b></a><a NAME="E1:32_3_1_2_3_1_2_7_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 0
 ;<br/><div class="add"><a NAME="E2:32_3_1_2_3_1_2_7_1_3"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T60">XREAL_1:60</a></i>;<br/><a NAME="E3:32_3_1_2_3_1_2_7_1_3"/><b>then </b><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="prepower.html#T13">PREPOWER:13</a></i>;<br/><span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 = 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="square_1.html#K3">^2</a> </span>)</span>
<b>by </b><i><a class="ref" href="power.html#T30">POWER:30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>

;<br/><a NAME="E5:32_3_1_2_3_1_2_7_1_3"/><b>then </b><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span></span>)</span>
 ;<br/><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 = 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K1">+</a> 1</span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="newton.html#T11">NEWTON:11</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>

;<br/><a NAME="E7:32_3_1_2_3_1_2_7_1_3"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="power.html#K3">to_power</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span>
 <b>by </b><i><a class="ref" href="power.html#T47">POWER:47</a></i>;<br/><a NAME="E8:32_3_1_2_3_1_2_7_1_3"/><b>then </b><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E5:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E31</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E9:32_3_1_2_3_1_2_7_1_3"/>
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="newton.html#K2">|^</a> 3</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E3:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E30</font></i></a>, <a class="txt" href="polyeq_1.html#E5:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E31</font></i></a>, <a class="txt" href="polyeq_1.html#E7:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E32</font></i></a>, <a class="ref" href="power.html#T30">POWER:30</a></i>;<br/><a NAME="E10:32_3_1_2_3_1_2_7_1_3"/><b>then </b><i><font color="Green">E34</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="txt" href="polyeq_1.html#E14:32_3_1_2_3_1_2"><i><font color="Green">E27</font></i></a></i>;<br/><a NAME="E11:32_3_1_2_3_1_2_7_1_3"/>
<span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="newton.html#K2">|^</a> 3 <a href="hidden.html#R1">=</a>  <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E14:32_3_1_2_3_1_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="polyeq_1.html#E8:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E33</font></i></a></i>;<br/><a NAME="E12:32_3_1_2_3_1_2_7_1_3"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="prepower.html#K4">-Root</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E29</font></i></a>, <a class="txt" href="polyeq_1.html#E10:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E34</font></i></a>, <a class="ref" href="prepower.html#D3">PREPOWER:def 3</a></i>;<br/><b>set </b><font color="Maroon">c<sub>11</sub></font> = <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span>;<br/><a NAME="E13:32_3_1_2_3_1_2_7_1_3"/><i><font color="Green">E36</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E10:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E34</font></i></a>, <a class="txt" href="polyeq_1.html#E12:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E35</font></i></a>, <a class="ref" href="power.html#D1">POWER:def 1</a></i>;<br/><a NAME="E14:32_3_1_2_3_1_2_7_1_3"/><i><font color="Green">E37</font></i>: 
3 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E15:32_3_1_2_3_1_2_7_1_3"/><b>then </b><i><font color="Green">E38</font></i>: 
 <a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K2">-root</a> <span class="p2">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E13:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E36</font></i></a>, <a class="ref" href="power.html#T12">POWER:12</a></i>;<br/><a NAME="E16:32_3_1_2_3_1_2_7_1_3"/>
3 <a href="power.html#K2">-root</a> <span class="p1">(<span class="default"><a href="real_1.html#K1">-</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 <b>by </b><i><a class="txt" href="polyeq_1.html#E14:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E37</font></i></a>, <a class="ref" href="power.html#T9">POWER:9</a></i>;<br/><a NAME="E17:32_3_1_2_3_1_2_7_1_3"/><b>then </b>
 <a href="xcmplx_0.html#K4">-</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E15:32_3_1_2_3_1_2_7_1_3"><i><font color="Green">E38</font></i></a></i>;<br/><b>hence </b><a NAME="E18:32_3_1_2_3_1_2_7_1_3"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> 3 <a href="power.html#K1">-root</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E17:32_3_1_2_3_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="polyeq_1.html#E2:32"><i><font color="Green">E9</font></i></a>, <a class="txt" href="polyeq_1.html#E21:32_3_1_2"><i><font color="Green">E22</font></i></a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E23:32_3_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E17:32"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> or <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default">3 <a href="power.html#K1">-root</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4">-</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K7">/</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K6">-</a> <span class="p3">(<span class="default"><a href="square_1.html#K6">sqrt</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="square_1.html#K3">^2</a> </span>)</span> <a href="xcmplx_0.html#K7">/</a> 4</span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> 3</span>)</span> <a href="newton.html#K2">|^</a> 3</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> )
 ;<br/>


</div>
